Explicit LDP for a slowed RW driven by a symmetric exclusion process

• 成果类型: Article
• 署名作者: Avena, L.; Jara, M.; Vollering, F.
• 署名单位: Leiden University; Leiden University - Excl LUMC; Instituto Nacional de Matematica Pura e Aplicada (IMPA); University of Bath
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-017-0797-6
• 发表日期: 2018
• 页码: 865-915
• 关键词: dynamic random-environments; large deviations; random-walk; additive-functionals; MARKOV-PROCESSES; limit; PRINCIPLE; particle

摘要

We consider a random walk (RW) driven by a simple symmetric exclusion process (SSE). Rescaling the RW and the SSE in such a way that a joint hydrodynamic limit theorem holds we prove a joint path large deviation principle. The corresponding large deviation rate function can be split into two components, the rate function of the SSE and the one of the RW given the path of the SSE. These components have different structures (Gaussian and Poissonian, respectively) and to overcome this difficulty we make use of the theory of Orlicz spaces. In particular, the component of the rate function corresponding to the RW is explicit.